Roxul is a rock-based mineral fiber insulation. Because of its moisture resistant and mildew resistant properties, its high R value, and the fact that it generates zero off-gases, it makes a great material for insulating coolers. Since it is not vapor resistant, you do need to add some rigid foam to the cooler. This rigid foam layer will also help stop thermal bridging, so it needs to be tacked to the outside edge of the stud, leaving the sheets of Styrofoam as large as possible. You would probably be fine with 3/4 inch, but going up to 1 or 1.5 inches would be even better. If you use 2 thinner layers you can stagger the seams so there are no gaps.